Problem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market to be able to payoff A when heexercises the option. (We assume that A exercises optimally.)(e) Now assume that A makes a mistake and doesn’t exercise optimally. What is theconsequence for you as the seller of the option ? (Only a short answer is required.
Problem 1.
We consider a two-period binomial model with the following properties: each period lasts
one (1) year and the current stock price is S0 = 4. On each period, the stock price doubles
when it moves up and is reduced by half when it moves down. The annual interest rate
on the money market is 25%.
We consider four options on this market:
A European call option with maturity T = 2 years and strike price K = 5;
A European put option with maturity T = 2 years and strike price K = 5;
An American call option with maturity T = 2 years and strike price K = 5;
An American put option with maturity T = 2 years and strike price K = 5.
(a) Find the price at time 0 of both European options.
(b) Find the price at time 0 of both American options. Compare your results with (a)
and comment.
(c) For each of the American options, describe the optimal exercising strategy.
(d) We assume that you sell the American put to a market participant A for the price
found in (b). Explain how you act on the market to be able to payoff A when he
exercises the option. (We assume that A exercises optimally.)
(e) Now assume that A makes a mistake and doesn’t exercise optimally. What is the
consequence for you as the seller of the option ? (Only a short answer is required.
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